The Effect Of Other Bodies On The Sun

If solar activity is really an important factor in causing climatic
changes, it behooves us to subject the sun to the same kind of inquiry
to which we have subjected the earth. We have inquired into the nature
of the changes through which the earth's crust, the oceans, and the
atmosphere have influenced the climate of geological times. It has not
been necessary, however, to study the origin of the earth, nor to trace
its earlier stages. Our study of the geological record begins only when
the earth had attained practically its present mass, essentially its
present shape, and a climate so similar to that of today that life as we
know it was possible. In other words, the earth had passed the stages of
infancy, childhood, youth, and early maturity, and had reached full
maturity. As it still seems to be indefinitely far from old age, we
infer that during geological times its relative changes have been no
greater than those which a man experiences between the ages of perhaps
twenty-five and forty.

Similar reasoning applies with equal or greater force to the sun.
Because of its vast size it presumably passes through its stages of
development much more slowly than the earth. In the first chapter of
this book we saw that the earth's relative uniformity of climate for
hundreds of millions of years seems to imply a similar uniformity in
solar activity. This accords with a recent tendency among astronomers
who are more and more recognizing that the stars and the solar system
possess an extraordinary degree of conservatism. Changes that once were
supposed to take place in thousands of years are now thought to have
required millions. Hence in this chapter we shall assume that throughout
geological times the condition of the sun has been almost as at present.
It may have been somewhat larger, or different in other ways, but it was
essentially a hot, gaseous body such as we see today and it gave out
essentially the same amount of energy. This assumption will affect the
general validity of what follows only if it departs widely from the
truth. With this assumption, then, let us inquire into the degree to
which the sun's atmosphere has probably been disturbed throughout
geological times.

In Earth and Sun, as already explained, a detailed study has led to
the conclusion that cyclonic storms are influenced by the electrical
action of the sun. Such action appears to be most intense in sunspots,
but apparently pertains also to other disturbed areas in the sun's
atmosphere. A study of sunspots suggests that their true periodicity is
almost if not exactly identical with that of the orbital revolution of
Jupiter, 11.8 years. Other investigations show numerous remarkable
coincidences between sunspots and the orbital revolution of the other
planets, including especially Saturn and Mercury. This seems to indicate
that there is some truth in the hypothesis that sunspots and other
related disturbances of the solar atmosphere owe their periodicity to
the varying effects of the planets as they approach and recede from the
sun in their eccentric orbits and as they combine or oppose their
effects according to their relative positions. This does not mean that
the energy of the solar disturbances is supposed to come from the
planets, but merely that their variations act like the turning of a
switch to determine when and how violently the internal forces of the
sun shall throw the solar atmosphere into commotion. This hypothesis is
by no means new, for in one form or another it has been advocated by
Wolfer, Birkeland, E. W. Brown, Schuster, Arctowski, and others.

The agency through which the planets influence the solar atmosphere is
not yet clear. The suggested agencies are the direct pull of
gravitation, the tidal effect of the planets, and an electro-magnetic
effect. In Earth and Sun the conclusion is reached that the first two
are out of the question, a conclusion in which E. W. Brown acquiesces.
Unless some unknown cause is appealed to, this leaves an
electro-magnetic hypothesis as the only one which has a reasonable
foundation. Schuster inclines to this view. The conclusions set forth in
Earth and Sun as to the electrical nature of the sun's influence on
the earth point somewhat in the same direction. Hence in this chapter we
shall inquire what would happen to the sun, and hence to the earth, on
their journey through space, if the solar atmosphere is actually subject
to disturbance by the electrical or other effects of other heavenly
bodies. It need hardly be pointed out that we are here venturing into
highly speculative ground, and that the verity or falsity of the
conclusions reached in this chapter has nothing to do with the validity
of the reasoning in previous chapters. Those chapters are based on the
assumption that terrestrial causes of climatic changes are supplemented
by solar disturbances which produce their effect partly through
variations in temperature but also through variations in the intensity
and paths of cyclonic storms. The present chapter seeks to shed some
light on the possible causes and sequence of solar disturbances.

Let us begin by scanning the available evidence as to solar disturbances
previous to the time when accurate sunspot records are available. Two
rather slender bits of evidence point to cycles of solar activity
lasting hundreds of years. One of these has already been discussed in
Chapter VI, where the climatic stress of the fourteenth century was
described. At that time sunspots are known to have been unusually
numerous, and there were great climatic extremes. Lakes overflowed in
Central Asia; storms, droughts, floods, and cold winters were unusually
severe in Europe; the Caspian Sea rose with great rapidity; the trees of
California grew with a vigor unknown for centuries; the most terrible of
recorded famines occurred in England and India; the Eskimos were
probably driven south by increasing snowiness in Greenland; and the
Mayas of Yucatan appear to have made their last weak attempt at a
revival of civilization under the stimulus of greater storminess and
less constant rainfall.

The second bit of evidence is found in recent exhaustive studies of
periodicities by Turner[112] and other astronomers. They have sought
every possible natural occurrence for which a numerical record is
available for a long period. The most valuable records appear to be
those of tree growth, Nile floods, Chinese earthquakes, and sunspots.
Turner reaches the conclusion that all four types of phenomena show the
same periodicity, namely, cycles with an average length of about 260 to
280 years. He suggests that if this is true, the cycles in tree growth
and in floods, both of which are climatic, are probably due to a
non-terrestrial cause. The fact that the sunspots show similar cycles
suggests that the sun's variations are the cause.

These two bits of evidence are far too slight to form the foundation of
any theory as to changes in solar activity in the geological past.
Nevertheless it may be helpful to set forth certain possibilities as a
stimulus to further research. For example, it has been suggested that
meteoric bodies may have fallen into the sun and caused it suddenly to
flare up, as it were. This is not impossible, although it does not
appear to have taken place since men became advanced enough to make
careful observations. Moreover, the meteorites which now fall on the
earth are extremely small, the average size being computed as no larger
than a grain of wheat. The largest ever found on the earth's surface, at
Bacubirito in Mexico, weighs only about fifty tons, while within the
rocks the evidences of meteorites are extremely scanty and
insignificant. If meteorites had fallen into the sun often enough and of
sufficient size to cause glacial fluctuations and historic pulsations of
climate, it seems highly probable that the earth would show much more
evidence of having been similarly disturbed. And even if the sun should
be bombarded by large meteors the result would probably not be sudden
cold periods, which are the most notable phenomena of the earth's
climatic history, but sudden warm periods followed by slow cooling.
Nevertheless, the disturbance of the sun by collision with meteoric
matter can by no means be excluded as a possible cause of climatic
variations.

Allied to the preceding hypothesis is Shapley's[113] nebular hypothesis.
At frequent intervals, averaging about once a year during the last
thirty years, astronomers have discovered what are known as novae. These
are stars which were previously faint or even invisible, but which flash
suddenly into brilliancy. Often their light-giving power rises seven or
eight magnitudes--a thousand-fold. In addition to the spectacular novae
there are numerous irregular variables whose brilliancy changes in every
ratio from a few per cent up to several magnitudes. Most of them are
located in the vicinity of nebulae, as is also the case with novae. This,
as well as other facts, makes it probable that all these stars are
"friction variables," as Shapley calls them. Apparently as they pass
through the nebulae they come in contact with its highly diffuse matter
and thereby become bright much as the earth would become bright if its
atmosphere were filled with millions of almost infinitesimally small
meteorites. A star may also lose brilliancy if nebulous matter
intervenes between it and the observer. If our sun has been subjected to
any of these changes some sort of climatic effect must have been
produced.

In a personal communication Shapley amplifies the nebular climatic
hypothesis as follows:

Within 700 light years of the sun in many directions (Taurus,
Cygnus, Ophiuchus, Scorpio) are great diffuse clouds of nebulosity,
some bright, most of them dark. The probability that stars moving in
the general region of such clouds will encounter this material is
very high, for the clouds fill enormous volumes of space,--e.g.,
probably more than a hundred thousand cubic light years in the Orion
region, and are presumably composed of rarefied gases or of dust
particles. Probably throughout all our part of space such nebulosity
exists (it is all around us, we are sure), but only in certain
regions is it dense enough to affect conspicuously the stars
involved in it. If a star moving at high velocity should collide
with a dense part of such a nebulous cloud, we should probably have
a typical nova. If the relative velocity of nebulous material and
star were low or moderate, or if the material were rare, we should
not expect a conspicuous effect on the star's light.

In the nebulous region of Orion, which is probably of unusually high
density, there are about 100 known stars, varying between 20% and
80% of their total light--all of them irregularly--some slowly, some
suddenly. Apparently they are "friction variables." Some of the
variables suddenly lose 40% of their light as if blanketed by
nebulous matter. In the Trifid Nebula there are variables like those
of Orion, in Messier 8 also, and probably many of the 100 or so
around the Rho Ophiuchi region belong to this kind.

I believe that our sun could not have been a typical nova, at least
not since the Archeozoic, that is for perhaps a billion years. I
believe we have in geological climates final proof of this, because
an increase in the amount of solar radiation by 1000 times as in the
typical nova, would certainly punctuate emphatically the life cycle
on the earth, even if the cause of the nova would not at the same
time eliminate the smaller planets. But the sun may have been one of
these miniature novae or friction variables; and I believe it very
probable that its wanderings through this part of space could not
long leave its mean temperature unaffected to the amount of a few
per cent.

One reason we have not had this proposal insisted upon before is
that the data back of it are mostly new--the Orion variables have
been only recently discovered and studied, the distribution and
content of the dark nebulae are hardly as yet generally known.

This interesting hypothesis cannot be hastily dismissed. If the sun
should pass through a nebula it seems inevitable that there would be at
least slight climatic effects and perhaps catastrophic effects through
the action of the gaseous matter not only on the sun but on the earth's
own atmosphere. As an explanation of the general climatic conditions of
the past, however, Shapley points out that the hypothesis has the
objection of being vague, and that nebulosity should not be regarded as
more than "a possible factor." One of the chief difficulties seems to be
the enormously wide distribution of as yet undiscovered nebulous matter
which must be assumed if any large share of the earth's repeated
climatic changes is to be ascribed to such matter. If such matter is
actually abundant in space, it is hard to see how any but the nearest
stars would be visible. Another objection is that there is no known
nebulosity near at hand with which to connect the climatic vicissitudes
of the last glacial period. Moreover, the known nebulae are so much less
numerous than stars that the chances that the sun will encounter one of
them are extremely slight. This, however, is not an objection, for
Shapley points out that during geological times the sun can never have
varied as much as do the novae, or even as most of the friction
variables. Thus the hypothesis stands as one that is worth
investigating, but that cannot be finally rejected or accepted until it
is made more definite and until more information is available.

Another suggested cause of solar variations is the relatively sudden
contraction of the sun such as that which sometimes occurs on the earth
when continents are uplifted and mountains upheaved. It seems improbable
that this could have occurred in a gaseous body like the sun. Lacking,
as it does, any solid crust which resists a change of form, the sun
probably shrinks steadily. Hence any climatic effects thus produced must
be extremely gradual and must tend steadily in one direction for
millions of years.

Still another suggestion is that the tidal action of the stars and other
bodies which may chance to approach the sun's path may cause
disturbances of the solar atmosphere. The vast kaleidoscope of space is
never quiet. The sun, the stars, and all the other heavenly bodies are
moving, often with enormous speed. Hence the effect of gravitation upon
the sun must vary constantly and irregularly, as befits the geological
requirements. In the case of the planets, however, the tidal effect does
not seem competent to produce the movements of the solar atmosphere
which appear to be concerned in the inception of sunspots. Moreover,
there is only the most remote probability that a star and the sun will
approach near enough to one another to produce a pronounced
gravitational disturbance in the solar atmosphere. For instance, if it
be assumed that changes in Jupiter's tidal effect on the sun are the
main factor in regulating the present difference between sunspot maxima
and sunspot minima, the chances that a star or some non-luminous body of
similar mass will approach near enough to stimulate solar activity and
thereby bring on glaciation are only one in twelve billion years, as
will be explained below. This seems to make a gravitational hypothesis
impossible.

Another possible cause of solar disturbances is that the stars in their
flight through space may exert an electrical influence which upsets the
equilibrium of the solar atmosphere. At first thought this seems even
more impossible than a gravitational effect. Electrostatic effects,
however, differ greatly from those of tides. They vary as the diameter
of a body instead of as its mass; their differentials also vary
inversely as the square of the distance instead of as the cube.
Electrostatic effects also increase as the fourth power of the
temperature or at least would do so if they followed the law of black
bodies; they are stimulated by the approach of one body to another; and
they are cumulative, for if ions arrive from space they must accumulate
until the body to which they have come begins to discharge them. Hence,
on the basis of assumptions such as those used in the preceding
paragraph, the chances of an electrical disturbance of the solar
atmosphere sufficient to cause glaciation on the earth may be as high as
one in twenty or thirty million years. This seems to put an electrical
hypothesis within the bounds of possibility. Further than that we cannot
now go. There may be other hypotheses which fit the facts much better,
but none seems yet to have been suggested.

In the rest of this chapter the tidal and electrical hypotheses of
stellar action on the sun will be taken up in detail. The tidal
hypothesis is considered because in discussions of the effect of the
planets it has hitherto held almost the entire field. The electrical
hypothesis will be considered because it appears to be the best yet
suggested, although it still seems doubtful whether electrical effects
can be of appreciable importance over such vast distances as are
inevitably involved. The discussion of both hypotheses will necessarily
be somewhat technical, and will appeal to the astronomer more than to

the layman. It does not form a necessary part of this book, for it has
no bearing on our main thesis of the effect of the sun on the earth. It
is given here because ultimately the question of changes in solar
activity during geological times must be faced.

In the astronomical portion of the following discussion we shall follow
Jeans[114] in his admirable attempt at a mathematical analysis of the
motions of the universe. Jeans divides the heavenly bodies into five
main types. (1) Spiral nebulae, which are thought by some astronomers to
be systems like our own in the making, and by others to be independent
universes lying at vast distances beyond the limits of our Galactic
universe, as it is called from the Galaxy or Milky Way. (2) Nebulae of a
smaller type, called planetary. These lie within the Galactic portion of
the universe and seem to be early stages of what may some day be stars
or solar systems. (3) Binary or multiple stars, which are
extraordinarily numerous. In some parts of the heavens they form 50 or
even 60 per cent of the stars and in the galaxy as a whole they seem to
form "fully one third." (4) Star clusters. These consist of about a
hundred groups of stars in each of which the stars move together in the
same direction with approximately the same velocity. These, like the
spiral nebulae, are thought by some astronomers to lie outside the limits
of the galaxy, but this is far from certain. (5) The solar system.
According to Jeans this seems to be unique. It does not fit into the
general mathematical theory by which he explains spiral nebulae,
planetary nebulae, binary stars, and star clusters. It seems to demand a
special explanation, such as is furnished by tidal disruption due to the
passage of the sun close to another star.

The part of Jeans' work which specially concerns us is his study of the
probability that some other star will approach the sun closely enough to
have an appreciable gravitative or electrical effect, and thus cause
disturbances in the solar atmosphere. Of course both the star and the
sun are moving, but to avoid circumlocution we shall speak of such
mutual approaches simply as approaches of the sun. For our present
purpose the most fundamental fact may be summed up in a quotation from
Jeans in which he says that most stars "show evidence of having
experienced considerable disturbance by other systems; there is no
reason why our solar system should be expected to have escaped the
common fate." Jeans gives a careful calculation from which it is
possible to derive some idea of the probability of any given degree of
approach of the sun and some other star. Of course all such calculations
must be based on certain assumptions. The assumptions made by Jeans are
such as to make the probability of close approaches as great as
possible. For example, he allows only 560 million years for the entire
evolution of the sun, whereas some astronomers and geologists would put
the figure ten or more times as high. Nevertheless, Jeans' assumptions
at least show the order of magnitude which we may expect on the basis of
reasonable astronomical conclusions.

According to the planetary hypothesis of sunspots, the difference in the
effect of Jupiter when it is nearest and farthest from the sun is the
main factor in starting the sunspot cycle and hence the corresponding
terrestrial cycle. The climatic difference between sunspot maxima and
minima, as measured by temperature, apparently amounts to at least a
twentieth and perhaps a tenth of the difference between the climate of
the last glacial epoch and the present. We may suppose, then, that a
body which introduced a gravitative or electrical factor twenty times as
great as the difference in Jupiter's effect at its maximum and minimum
distances from the sun would cause a glacial epoch if the effect lasted
long enough. Of course the other planets combine their effects with that
of Jupiter, but for the sake of simplicity we will leave the others out
of account. The difference between Jupiter's maximum and minimum tidal
effect on the sun amounts to 29 per cent of the planet's average effect.
The corresponding difference, according to the electrical hypothesis, is
about 19 per cent, for electrostatic action varies as the square of the
distance instead of as the cube. Let us assume that a body exerting four
times Jupiter's present tidal effect and placed at the average distance
of Jupiter from the sun would disturb the sun's atmosphere twenty times
as much as the present difference between sunspot maxima and minima, and
thus, perhaps, cause a glacial period on the earth.

On the basis of this assumption our first problem is to estimate the
frequency with which a star, visible or dark, is likely to approach near
enough to the sun to produce a tidal effect four times that of
Jupiter. The number of visible stars is known or at least well
estimated. As to dark stars, which have grown cool, Arrhenius believed
that they are a hundred times as numerous as bright stars; few
astronomers believe that there are less than three or four times as
many. Dr. Shapley of the Harvard Observatory states that a new
investigation of the matter suggests that eight or ten is probably a
maximum figure. Let us assume that nine is correct. The average visible
star, so far as measured, has a mass about twice that of the sun, or
about 2100 times that of Jupiter. The distances of the stars have been
measured in hundreds of cases and thus we can estimate how many stars,
both visible and invisible, are on an average contained in a given
volume of space. On this basis Jeans estimates that there is only one
chance in thirty billion years that a visible star will approach within
2.8 times the distance of Neptune from the sun, that is, within about
eight billion miles. If we include the invisible stars the chances
become one in three billion years. In order to produce four times the
tidal effect of Jupiter, however, the average star would have to
approach within about four billion miles of the sun, and the chances of
that are only one in twelve billion years. The disturbing star would be
only 40 per cent farther from the sun than Neptune, and would almost
pass within the solar system.

Even though Jeans holds that the frequency of the mutual approach of the
sun and a star was probably much greater in the distant past than at
present, the figures just given lend little support to the tidal
hypothesis. In fact, they apparently throw it out of court. It will be
remembered that Jeans has made assumptions which give as high a
frequency of stellar encounters as is consistent with the astronomical
facts. We have assumed nine dark stars for every bright one, which may
be a liberal estimate. Also, although we have assumed that a disturbance
of the sun's atmosphere sufficient to cause a glacial period would arise
from a tidal effect only twenty times as great as the difference in
Jupiter's effect when nearest the sun and farthest away, in our
computations this has actually been reduced to thirteen. With all these
favorable assumptions the chances of a stellar approach of the sort here
described are now only one in twelve billion years. Yet within a hundred
million years, according to many estimates of geological time, and
almost certainly within a billion, there have been at least half a dozen
glaciations.

Our use of Jeans' data interposes another and equally insuperable
difficulty to any tidal hypothesis. Four billion miles is a very short
distance in the eyes of an astronomer. At that distance a star twice the
size of the sun would attract the outer planets more strongly than the
sun itself, and might capture them. If a star should come within four
billion miles of the sun, its effect in distorting the orbits of all the
planets would be great. If this had happened often enough to cause all
the glaciations known to geologists, the planetary orbits would be
strongly elliptical instead of almost circular. The consideration here
advanced militate so strongly against the tidal hypothesis of solar
disturbances that it seems scarcely worth while to consider it further.

Let us turn now to the electrical hypothesis. Here the conditions are
fundamentally different from those of the tidal hypothesis. In the first
place the electrostatic effect of a body has nothing to do with its
mass, but depends on the area of its surface; that is, it varies as the
square of the radius. Second, the emission of electrons varies
exponentially. If hot glowing stars follow the same law as black bodies
at lower temperatures, the emission of electrons, like the emission of
other kinds of energy, varies as the fourth power of the absolute
temperature. In other words, suppose there are two black bodies,
otherwise alike, but one with a temperature of 27 deg. C. or 300 deg. on the
absolute scale, and the other with 600 deg. on the absolute scale. The
temperature of one is twice as high as that of the other, but the
electrostatic effect will be sixteen times as great.[115] Third, the
number of electrons that reach a given body varies inversely as the
square of the distance, instead of as the cube which is the case with
tide-making forces.

In order to use these three principles in calculating the effect of the
stars we must know the diameters, distances, temperature, and number of
the stars. The distances and number may safely be taken as given by
Jeans in the calculations already cited. As to the diameters, the
measurements of the stars thus far made indicate that the average mass
is about twice that of the sun. The average density, as deduced by
Shapley[116] from the movements of double stars, is about one-eighth the
solar density. This would give an average diameter about two and a half
times that of the sun. For the dark stars, we shall assume for
convenience that they are ten times as numerous as the bright ones. We
shall also assume that their diameter is half that of the sun, for being
cool they must be relatively dense, and that their temperature is the
same as that which we shall assume for Jupiter.

As to Jupiter we shall continue our former assumption that a body with
four times the effectiveness of that planet, which here means with twice
as great a radius, would disturb the sun enough to cause glaciation. It
would produce about twenty times the electrostatic effect which now
appears to be associated with the difference in Jupiter's effect at
maximum and minimum. The temperature of Jupiter must also be taken into
account. The planet is supposed to be hot because its density is low,
being only about 1.25 that of water. Nevertheless, it is probably not
luminous, for as Moulton[117] puts it, shadows upon it are black and its
moons show no sign of illumination except from the sun. Hence a
temperature of about 600 deg.C., or approximately 900 deg. on the absolute
scale, seems to be the highest that can reasonably be assigned to the
cold outer layer whence electrons are emitted. As to the temperature of
the sun, we shall adopt the common estimate of about 6300 deg.C. on the
absolute scale. The other stars will be taken as averaging the same,
although of course they vary greatly.

When Jeans' method of calculating the probability of a mutual approach
of the sun and a star is applied to the assumptions given above, the
results are as shown in Table 5. On that basis the dark stars seem to be
of negligible importance so far as the electrical hypothesis is
concerned. Even though they may be ten times as numerous as the bright
ones there appears to be only one chance in 130 billion years that one
of them will approach the sun closely enough to cause the assumed
disturbance of the solar atmosphere. On the other hand, if all the
visible stars were the size of the sun, and as hot as that body, their
electrical effect would be fourfold that of our assumed dark star
because of their size, and 2401 times as great because of their
temperature, or approximately 10,000 times as great. Under such
conditions the theoretical chance of an approach that would cause
glaciation is one in 130 million years. If the average visible star is
somewhat cooler than the sun and has a radius about two and one-half
times as great, as appears to be the fact, the chances rise to one in
thirty-eight million years. A slight and wholly reasonable change in our
assumptions would reduce this last figure to only five or ten million.
For instance, the earth's mean temperature during the glacial period has
been assumed as 10 deg.C. lower than now, but the difference may have been
only 6 deg.. Again, the temperature of the outer atmosphere of Jupiter where
the electrons are shot out may be only 500 deg. or 700 deg. absolute, instead of
900 deg.. Or the diameter of the average star may be five or ten times that
of the sun, instead of only two and one-half times as great. All this,
however, may for the present be disregarded. The essential point is that
even when the assumptions err on the side of conservatism, the results
are of an order of magnitude which puts the electrical hypothesis within
the bounds of possibility, whereas similar assumptions put the tidal
hypothesis, with its single approach in twelve billion years, far beyond
those limits.

The figures for Betelgeuse in Table 5 are interesting. At a meeting of
the American Association for the Advancement of Science in December,
1920, Michelson reported that by measurements of the interference of
light coming from the two sides of that bright star in Orion, the
observers at Mount Wilson had confirmed the recent estimates of three
other authorities that the star's diameter is about 218 million miles,
or 250 times that of the sun. If other stars so much surpass the
estimates of only a decade or two ago, the average diameter of all the
visible stars must be many times that of the sun. The low figure for
Betelgeuse in section D of the table means that if all the stars were as
large as Betelgeuse, several might often be near enough to cause
profound disturbances of the solar atmosphere. Nevertheless, because of
the low temperature of the giant red stars of the Betelgeuse type, the
distance at which one of them would produce a given electrical effect is
only about five times the distance at which our assumed average star
would produce the same effect. This, to be sure, is on the assumption
that the radiation of energy from incandescent bodies varies according
to temperature in the same ratio as the radiation from black bodies.
Even if this assumption departs somewhat from the truth, it still seems
almost certain that the lower temperature of the red compared with the
high temperature of the white stars must to a considerable degree reduce
the difference in electrical effect which would otherwise arise from
their size.

D. Average
interval between
approaches
close enough to
cause glaciation
if all stars 130,000,000,000
were of given [119]
type. Years. 130,000,00038,000,000 700,000
---------------------------------------------------------------------

Thus far in our attempt to estimate the distance at which a star might
disturb the sun enough to cause glaciation on the earth, we have
considered only the star's size and temperature. No account has been
taken of the degree to which its atmosphere is disturbed. Yet in the
case of the sun this seems to be one of the most important factors. The
magnetic field of sunspots is sometimes 50 or 100 times as strong as
that of the sun in general. The strength of the magnetic field appears
to depend on the strength of the electrical currents in the solar
atmosphere. But the intensity of the sunspots and, by inference, of the
electrical currents, may depend on the electrical action of Jupiter and
the other planets. If we apply a similar line of reasoning to the stars,
we are at once led to question whether the electrical activity of double
stars may not be enormously greater than that of isolated stars like the
sun.

If this line of reasoning is correct, the atmosphere of every double
star must be in a state of commotion vastly greater than that of the
sun's atmosphere even when it is most disturbed. For example, suppose
the sun were accompanied by a companion of equal size at a distance of
one million miles, which would make it much like many known double
stars. Suppose also that in accordance with the general laws of physics
the electrical effect of the two suns upon one another is proportional
to the fourth power of the temperature, the square of the radius, and
the inverse square of the distance. Then the effect of each sun upon the
other would be sixty billion (6 x 10^{10}) times as great as the present
electrical effect of Jupiter upon the sun. Just what this would mean as
to the net effect of a pair of such suns upon the electrical potential
of other bodies at a distance we can only conjecture. The outstanding
fact is that the electrical conditions of a double star must be
radically different and vastly more intense than those of a single star
like the sun.

This conclusion carries weighty consequences. At present twenty or more
stars are known to be located within about 100 trillion miles of the sun
(five parsecs, as the astronomers say), or 16.5 light years. According
to the assumptions employed in Table 5 an average single star would
influence the sun enough to cause glaciation if it came within
approximately 200 billion miles. If the star were double, however, it
might have an electrical capacity enormously greater than that of the
sun. Then it would be able to cause glaciation at a correspondingly
great distance. Today Alpha Centauri, the nearest known star about
twenty-five trillion miles, or 4.3 light years from the sun, and Sirius,
the brightest star in the heavens, is about fifty trillion miles away,
or 8.5 light years. If these stars were single and had a diameter three
times that of the sun, and if they were of the same temperature as has
been assumed for Betelgeuse, which is about fifty times as far away as
Alpha Centauri, the relative effects of the three stars upon the sun
would be, approximately, Betelgeuse 700, Alpha Centauri 250, Sirius 1.
But Alpha Centauri is triple and Sirius double, and both are much hotter
than Betelgeuse. Hence Alpha Centauri and even Sirius may be far more
effective than Betelgeuse.

The two main components of Alpha Centauri are separated by an average
distance of about 2,200,000,000 miles, or somewhat less than that of
Neptune from the sun. A third and far fainter star, one of the faintest
yet measured, revolves around them at a great distance. In mass and
brightness the two main components are about like the sun, and we will
assume that the same is true of their radius. Then, according to the
assumptions made above, their effect in disturbing one another
electrically would be about 10,000 times the total effect of Jupiter
upon the sun, or 2500 times the effect that we have assumed to be
necessary to produce a glacial period. We have already seen in Table 5
that, according to our assumptions, a single star like the sun would
have to approach within 120 billion miles of the solar system, or within
2 per cent of a light year, in order to cause glaciation. By a similar
process of reasoning it appears that if the mutual electrical excitation
of the two main parts of Alpha Centauri, regardless of the third part,
is proportional to the apparent excitation of the sun by Jupiter, Alpha
Centauri would be 5000 times as effective as the sun. In other words, if
it came within 8,500,000,000,000 miles of the sun, or 1.4 light years,
it would so change the electrical conditions as to produce a glacial
epoch. In that case Alpha Centauri is now so near that it introduces a
disturbing effect equal to about one-sixth of the effect needed to cause
glaciation on the earth. Sirius and perhaps others of the nearer and
brighter or larger stars may also create appreciable disturbances in the
electrical condition of the sun's atmosphere, and may have done so to a
much greater degree in the past, or be destined to do so in the future.
Thus an electrical hypothesis of solar disturbances seems to indicate
that the position of the sun in respect to other stars may be a factor
of great importance in determining the earth's climate.

[Footnote 115: This fact is so important and at the same time so
surprising to the layman, that a quotation from The Electron Theory of
Matter by O. W. Richardson, 1914, pp. 326 and 334 is here added.

"It is a very familiar fact that when material bodies are heated they
emit electromagnetic radiations, in the form of thermal, luminous, and
actinic rays, in appreciable quantities. Such an effect is a natural
consequence of the electron and kinetic theories of matter. On the
kinetic theory, temperature is a measure of the violence of the motion
of the ultimate particles; and we have seen that on the electron theory,
electromagnetic radiation is a consequence of their acceleration. The
calculation of this emission from the standpoint of the electron theory
alone is a very complex problem which takes us deeply into the structure
of matter and which has probably not yet been satisfactorily resolved.
Fortunately, we can find out a great deal about these phenomena by the
application of general principles like the conservation of energy and
the second law of thermodynamics without considering special assumptions
about the ultimate constitution of matter. It is to be borne in mind
that the emission under consideration occurs at all temperatures
although it is more marked the higher the temperature.... The energy per
unit volume, in vacuo, of the radiation in equilibrium in an enclosure
at the absolute temperature, T, is equal to a universal constant, A,
multiplied by the fourth power of the absolute temperature. Since the
intensity of the radiation is equal to the energy per unit volume
multiplied by the velocity of light, it follows that the former must
also be proportional to the fourth power of the absolute temperature.
Moreover, if E is the total emission from unit area of a perfectly black
body, we see from p. 330 that E=A'T^{4}, where A' is a new universal
constant. This result is usually known as Stefan's Law. It was suggested
by Stefan in the inaccurate form that the total radiant energy of
emission from bodies varies as the fourth power of the absolute
temperature, as a generalization from the results of experiments. The
credit for showing that it is a consequence of the existence of
radiation pressure combined with the principles of thermodynamics is due
to Bartoli and Boltzmann."]

[Footnote 116: Quoted by Moulton in his Introduction to Astronomy.]

[Footnote 117: Introduction to Astronomy.]

[Footnote 118: The term billions, here and elsewhere, is used in the
American sense, 10^{9}.]

[Footnote 119: The assumed number of stars here is ten times as great as
in the other parts of this line.]